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Multiply (6 cis 300o)(2 cis 30o) and express the answer in rectangular form.

I know how to express this in polar form, but how do I put it into rectangular form?

Shades  Dec 3, 2015

Best Answer 

 #1
avatar+90996 
+15

Hi Shades :)

 

Multiply (6 cis 300o)(2 cis 30o) and express the answer in rectangular form. {nl} {nl} I know how to express this in polar form, but how do I put it into rectangular form?

 

 

\( (6 e^{300^{0}i})*(2e^{30^0i})\\~\\ =12e^{330^0i}\\~\\ =12(cos330+isin330)\\~\\ =12(cos30-isin30))\\~\\ =12(\frac{\sqrt3}{2}-i*\frac{1}{2})\\~\\ =6\sqrt3-6i\)

Melody  Dec 3, 2015
edited by Melody  Dec 3, 2015
edited by Melody  Dec 5, 2015
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6+0 Answers

 #1
avatar+90996 
+15
Best Answer

Hi Shades :)

 

Multiply (6 cis 300o)(2 cis 30o) and express the answer in rectangular form. {nl} {nl} I know how to express this in polar form, but how do I put it into rectangular form?

 

 

\( (6 e^{300^{0}i})*(2e^{30^0i})\\~\\ =12e^{330^0i}\\~\\ =12(cos330+isin330)\\~\\ =12(cos30-isin30))\\~\\ =12(\frac{\sqrt3}{2}-i*\frac{1}{2})\\~\\ =6\sqrt3-6i\)

Melody  Dec 3, 2015
edited by Melody  Dec 3, 2015
edited by Melody  Dec 5, 2015
 #2
avatar+466 
+5

That's exactly how it is supposed to look at the end. Thank you very much! cool

Shades  Dec 3, 2015
 #3
avatar+90996 
+5

You are very welcome Shades :)

 

You probably already have a good text book but I found this online.  Maybe it will be helpful.

https://www.adelaide.edu.au/mathslearning/bridging/resources/MT5ComplexBook_Feb2013.pdf

Melody  Dec 3, 2015
 #4
avatar+78577 
+5

Very nice, Melody !!!

 

 

cool cool cool

CPhill  Dec 3, 2015
 #5
avatar+466 
0

A quick question, why are we simplifying the angles to 30o instead of 60o? 330o is 600 more than 270o so wouldn't the angles be simplified to 60o?

Shades  Dec 4, 2015
 #6
avatar+90996 
0

Thanks Chris . :D

 

I have answered Shades's  last question  - he must have posted it somewhere else :/

Melody  Dec 5, 2015

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